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Explicit Brauer-Manin for a 9-Nodal Cubic 3-Fold

Brett Frankel

Northwestern University

Location

University of Pennsylvania

DRL 4N30

Note the special tie due to the double header Galois seminar on March 17

We will review the theory of Brauer-Manin obstructions to the Hasse principle, then discuss what is known about the Hasse principle for cubic threefolds with isolated singularities. In particular, Shepherd-Barron classified 9-nodal cubic 3-folds and proved that the only obstruction to the Hasse principle for these 3-folds is the Brauer-Manin obstruction. Building on the work of Shepherd-Barron, we write down an explicit example of a 9-nodal cubic 3-fold violating the Hasse principle. This is work in progress joint with Anastassia Etropolski and Marta Pieropan.

How to get to Penn's Mathematics Department

The Mathematics Department Office is located on the fourth (top) floor of David Rittenhouse Laboratory ("DRL"). The building is at 209 South 33rd Street (the Southeast corner of 33rd. and Walnut Streets). Note 33rd Street runs one way northwhile Walnut runs one waywest.

We are about a 15 minute walk from the main 30th Street Station and 5 minutes from the University City Rail Station at 32nd and Spruce (=South Street & Convention Avenue). Coming from the airport by train (about 15 minutes): the University City Rail Station is the second stop after you leave the airport.

If you drive, the most convenient public parking is in the pay lot whose entrance is on 34th Street between Market and Chestnut Streets.